Abel was a son of Abigail Hicks and Moses Eastabrooks, from Warren, Rhode Island. He had 8 siblings: Cynthia, Eliza, Lucy, Levi, Barnard, Abigail, John and Stephen. He married Catharine Frisbie in October of 1815. They had 4 children: Charles, Laura, Aaron Gaylord and Levi Frisbie.

Catharine died in 1822, Abel then married Dorcas Catlin in Bradford Pennsylvania. They had 5 children: Nathaniel Catlin, Mahlon D., Catherine, George and Ira.